We investigate nonperturbative features of a planar lattice Chem-Simon
s gauge theory modeling the physics of Josephson junction arrays. By i
dentifying the relevant topological configurations and their interacti
ons, we determine the phase structure of the model. Our results match
observed phase transitions in Josephson junction arrays and suggest al
so the possibility of oblique confining ground states corresponding to
purely planar quantum Hall regimes for either charges or vortices.